Answer to Question #165814 in Electrical Engineering for Enthada Nokkunne

Question

Two coils A and B are connected in series across a 110V, 60Hz supply. The resistance of coil A is 2  and inductance of coil B is 0.004H. If the input from the supply is 2.4kW and 1.8kVAR, find the inductance of coil A and resistance of coil B. Also calculate the voltage across each coil.

Answer 1

The frequency is 60 Hz, so, the reactance of the second coil is

$$X_{2}=2\pi fL_2=1.5\space\Omega.$$

So, since the total voltage is 110 V, the connection is series, and the active power output is 2400 W:

$$P=\frac{V^2}{R_1+R_2},\\\space\\ R_2=\frac{V^2}{P}-R_1=3.04\space\Omega.$$

The voltage across the first one:

$$V_1=IR_1=\frac{V}{R_1+R_2}R_1=43.7\text{ V},\\\space\\ V_2=IR_2=\frac{V}{R_1+R_2}R_2=66.3\text{ V}.$$

Find the power factor:

$$\text{ cos}\phi=\frac{P}{\sqrt{P^2+Q^2}}=0.8.$$

The reactance of the first coil can be found from the following:

$$\text{cos}\phi=\frac{R_1+R_2}{\sqrt{(R_1+R_2)^2+(X_1+X_2)^2}},\\\space\\ X_1=\sqrt{\bigg(\frac{R_1+R_2}{\text{cos}\phi}\bigg)^2-(R_1+R_2)^2}-X_2=2.28\space\Omega,\\\space\\ L_1=\frac{X_1}{2\pi f}=0.006\text{ H}.$$